(ns pe.p11)

(def grid-dim 20)

(def grid [
  8 2 22 97 38 15 0 40 0 75 4 5 7 78 52 12 50 77 91 8
  49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 4 56 62 0
  81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 3 49 13 36 65
  52 70 95 23 4 60 11 42 69 24 68 56 01 32 56 71 37 2 36 91
  22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
  24 47 32 60 99 3 45 2 44 75 33 53 78 36 84 20 35 17 12 50
  32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
  67 26 20 68 2 62 12 20 95 63 94 39 63 8 40 91 66 49 94 21
  24 55 58 5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
  21 36 23 9 75 0 76 44 20 45 35 14 0 61 33 97 34 31 33 95
  78 17 53 28 22 75 31 67 15 94 3 80 4 62 16 14 9 53 56 92
  16 39 5 42 96 35 31 47 55 58 88 24 0 17 54 24 36 29 85 57
  86 56 0 48 35 71 89 7 5 44 44 37 44 60 21 58 51 54 17 58
  19 80 81 68 5 94 47 69 28 73 92 13 86 52 17 77 4 89 55 40
  4 52 8 83 97 35 99 16 7 97 57 32 16 26 26 79 33 27 98 66
  88 36 68 87 57 62 20 72 3 46 33 67 46 55 12 32 63 93 53 69
  4 42 16 73 38 25 39 11 24 94 72 18 8 46 29 32 40 62 76 36
  20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 4 36 16
  20 73 35 29 78 31 90 1 74 31 49 71 48 86 81 16 23 57 5 54
  1 70 54 71 83 51 54 69 16 92 33 48 61 43 52 1 89 19 67 48])

(defn grid-value [x y]
  {:pre [(>= x 0) (< x grid-dim) (>= y 0) (< y grid-dim)]}
  (grid (+ (* grid-dim y) x)))

(def down [0 1])
(def right [1 0])
(def left-diag [-1 1])
(def right-diag [1 1])
(def dirs [down right left-diag right-diag])

(defn next-point [pt dir]
  (let [[x y] pt [dx dy] dir]
    [(+ x dx) (+ y dy)]))

(defn path-from-dir [pt dir len path]
  (let [[x y] pt]
    (cond
      (= len (count path)) path
      (>= x grid-dim) path
      (>= y grid-dim) path
      (< y 0) path
      (< x 0) path
      :else (recur (next-point pt dir) dir len (conj path (grid-value x y))))))

(defn coords [] (range grid-dim))

(defn all-paths [n]
  (filter #(= n (count %))
    (for [y (coords) x (coords) dir dirs] (path-from-dir [x y] dir n []))))

(defn path-length [path] (reduce * path))

(println (reduce max (map path-length (all-paths 4))))


